The authors of the article note several similarities with the bizarre and enigmatic soft-bodied life forms that lived between 635 and 540 million years ago - the span of Earth history known as the Ediacaran Period.

We think it belongs in the animal kingdom somewhere, the question is whereJorgen Olesen, University of Copenhagen

These organisms, too, have proven difficult to categorise and some researchers have even suggested they were failed experiments in multi-cellular life.

The authors of the paper recognise two new species of mushroom-shaped animal: Dendrogramma enigmatica and Dendrogramma discoides. Measuring only a few millimetres in size, the animals consist of a flattened disc and a stalk with a mouth on the end.

During a scientific cruise in 1986, scientists collected organisms at water depths of 400m and 1,000m on the south-east Australian continental slope, near Tasmania. But the two types of mushroom-shaped organisms were recognised only recently, after sorting of the bulk samples collected during the expedition.

"Finding something like this is extremely rare, it's maybe only happened about four times in the last 100 years," said co-author Jorgen Olesen from the University of Copenhagen.

He told BBC News: "We think it belongs in the animal kingdom somewhere; the question is where."

The system used to group every life form on Earth encompasses several levels, or taxonomic ranks.

A domain is the highest taxonomic rank and below that is a kingdom. Traditionally, biologists have recognised five or six kingdoms, including animals, plants, fungi and bacteria.

Kingdoms are divided into phyla, which are grouped according to similarities in general body plan.

They resemble organisms from the Ediacaran Period, many of which were thought to be evolutionary dead-ends

"What we can say about these organisms is that they do not belong with the bilateria," said Dr Olesen.

Bilateria represents one of the most important animal groupings, whose members share bilateral symmetry (their bodies are divided vertically into left and right halves that mirror one another). Humans belong within this grouping.

The new organisms are multicellular but mostly non-symmetrical, with a dense layer of gelatinous material between the outer skin cell and inner stomach cell layers.

The researchers did find some similarities to other animal groupings, such as the Cnidaria - the phylum that comprises corals and jellyfish - and the Ctenophora, which includes the marine organisms known as comb jellies. But the new organisms did not fulfil all the criteria required for inclusion in either of those categories.

Dr Olesen said the new animals could either be a very early branch on the tree of life, or be intermediate between two different animal phyla.

He conceded that they might eventually find their way into an existing group, because there was still so little known about Dendrogramma's biology.

One way to resolve the question surrounding Dendrogramma's affinities would be to examine its DNA, but new specimens will need to be found. The original samples were first preserved in formaldehyde and later transferred to 80% alcohol, a mode of treatment that prevents analysis of genetic material.

Accordingly, the team's paper in Plos One calls for researchers around the world to keep an eye out for other examples.